A criterion for the transition between flow regimes in turbulent cavity flow.
Pressure coefficient criterion for transition between two- and three-dimensional turbulent cavity flow
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Calculation of Turbine Axial Thrust by Coupled CFD Simulations of the Main Flow Path and Secondary Cavity Flow in an SLI LOX Turbine
Each single reusable Space Launch Initiative (SLI) booster rocket is an engine operating at a record vacuum thrust level of over 730,000 Ibf using LOX and LH2. This thrust is more than 10% greater than that of the Delta IV rocket, resulting in relatively large LOX and LH2 turbopumps. Since the SLI rocket employs a staged combustion cycle the level of pressure is very high (thousands of psia). This high pressure creates many engineering challenges, including the balancing of axial-forces on the turbopumps. One of the main parameters in the calculation of the axial force is the cavity pressure upstream of the turbine disk. The flow in this cavity is very complex. The lack of understanding of this flow environment hinders the accurate prediction of axial thrust. In order to narrow down the uncertainty band around the actual turbine axial force, a coupled, unsteady computational methodology has been developed to simulate the interaction between the turbine main flow path and the cavity flow. The CORSAIR solver, an unsteady three- dimensional Navier-Stokes code for turbomachinery applications, was used to solve for both the main and the secondary flow fields. Turbine axial thrust values are presented in conjunction with the CFD simulation, together with several considerations regarding the turbine instrumentation for axial thrust estimations during test.
Dorney, D. J.↗
Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow
Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.
Chen, C.-J.↗
Experimental Investigation of Porous-floor Effects on Cavity Flow Fields at Supersonic Speeds
An experimental investigation was conducted to determine the effectiveness of a passive-venting system to modify the flow field characteristics of a rectangular-box cavity at supersonic speeds. The passive-venting system consists of a porous floor with a vent chamber beneath the floor. For certain cavity length-to-height ratios, this configuration allowed high-pressure air at the rear of the cavity to vent to the forward part of the cavity, thereby modifying the cavity flow field. The wind-tunnel model consisted of a flat plate that housed a cavity mounted on a balance such that only the cavity drag was measured. The cavity height remained constant, and the length varied with rectangular-block inserts. Both solid-and porous-floor cavities were tested for comparison at Mach numbers of 1.60, 1.90, 2.16, and 2.86. These results showed that the passive-venting system did modify the cavity flow field. In order to determine the type flow field which existed for the porous-floor configuration, pressures were measured inside the cavity at the same conditions and for the same configurations as those used in the drag tests. Pressure data were also obtained with stores mounted in the cavity. These results, along with Schlieren photographs and the tabulated data, are presented to document the porous-floor cavity flow field.
Wilcox, Floyd J., Jr.↗
Study of three-dimensional cavity flow at transonic speeds
The present investigation of cavity flow in the subsonic and transonic speed regimes gives attention to the effect of Reynolds number on the flow inside the cavity. A rectangular, three-dimensional cavity was tested over Mach 0.3-1.05, and at Reynolds number/foot from 1 million to 4.2 million; two different cavity sizes were tested. For the deeper of the two cavities, at low Reynolds number, and for all conditions tested with the shallow cavity, the data showed much less steadiness. The results also show that the shallow cavity static pressure measurements were sensitive to the thickness of the boundary layer entering the cavity.
Plentovich, E. B.↗
Turbomachine Sealing and Secondary Flows - Part 3: Review of Power-Stream Support, Unsteady Flow Systems, Seal and Disk Cavity Flows, Engine Externals, and Life and Reliability Issues - Part 3
The issues and components supporting the engine power stream are reviewed. It is essential that companies pay close attention to engine sealing issues, particularly on the high-pressure spool or high-pressure pumps. Small changes in these systems are reflected throughout the entire engine. Although cavity, platform, and tip sealing are complex and have a significant effect on component and engine performance, computational tools (e.g., NASA-developed INDSEAL, SCISEAL, and ADPAC) are available to help guide the designer and the experimenter. Gas turbine engine and rocket engine externals must all function efficiently with a high degree of reliability in order for the engine to run but often receive little attention until they malfunction. Within the open literature statistically significant data for critical engine components are virtually nonexistent; the classic approach is deterministic. Studies show that variations with loading can have a significant effect on component performance and life. Without validation data they are just studies. These variations and deficits in statistical databases require immediate attention.
Hendricks, R. C.↗
Effects of Shrouded Stator Cavity Flows on Multistage Axial Compressor Aerodynamic Performance
Experiments were performed on a low-speed multistage axial-flow compressor to assess the effects of shrouded stator cavity flows on aerodynamic performance. Five configurations, which involved changes in seal-tooth leakage rates and/or elimination of the shrouded stator cavities, were tested. Data collected enabled differences in overall individual stage and the third stage blade element performance parameters to be compared. The results show conclusively that seal-tooth leakage ran have a large impact on compressor aerodynamic performance while the presence of the shrouded stator cavities alone seemed to have little influence. Overall performance data revealed that for every 1% increase in the seal-tooth clearance to blade-height ratio the pressure rise dropped up to 3% while efficiency was reduced by 1 to 1.5 points. These observed efficiency penalty slopes are comparable to those commonly reported for rotor and cantilevered stator tip clearance variations. Therefore, it appears that in order to correctly predict overall performance it is equally important to account for the effects of seal-tooth leakage as it is to include the influence of tip clearance flows. Third stage blade element performance data suggested that the performance degradation observed when leakage was increased was brought about in two distinct ways. First, increasing seal-tooth leakage directly spoiled the near hub performance of the stator row in which leakage occurred. Second, the altered stator exit now conditions caused by increased leakage impaired the performance of the next downstream stage by decreasing the work input of the downstream rotor and increasing total pressure loss of the downstream stator. These trends caused downstream stages to progressively perform worse. Other measurements were acquired to determine spatial and temporal flow field variations within the up-and-downstream shrouded stator cavities. Flow within the cavities involved low momentum fluid traveling primarily in the circumferential direction at about 40% of the hub wheel speed. Measurements indicated that the flow within both cavities was much more complex than first envisioned. A vortical flow structure in the meridional plane, similar to a driven cavity, existed within the upstream cavity Furthermore, other spatial and temporal variations in Row properties existed. the most prominent being caused by the upstream potential influence of the downstream blade. This influence caused the fluid within cavities near the leading edges of either stator blades in space or rotor blades in time to be driven radially inward relative to fluid near blade mid-pitch. This influence also produced large unsteady velocity fluctuations in the downstream cavity because of the passing of the downstream rotor blade.
Wellborn, Steven R.↗
A vortex model of cavity flow
The paper presents a model of two-dimensional cavity flow in which the shear layer over the cavity is represented by discrete rectilinear vortices which are free to move as the flow progresses. Although the model is initially started impulsively, the computation is continued until a statistically steady flow is attained. The broadband noise generation of the cavity is calculated by first running the model until the steady state is reached and then computing a stationary record of far-field density fluctuation through an equation that is suitable for calculating the quadrupole noise generation by the model. The discrete time series obtained can be analyzed by ordinary digital spectral techniques to determine the spectra and overall levels of the noise in airframe noise testing of real aircraft.
Hardin, J. C.↗
Multigrid Approach to Incompressible Viscous Cavity Flows
Two-dimensional incompressible viscous driven-cavity flows are computed for Reynolds numbers on the range 100-20,000 using a loosely coupled, implicit, second-order centrally-different scheme. Mesh sequencing and three-level V-cycle multigrid error smoothing are incorporated into the symmetric Gauss-Seidel time-integration algorithm. Parametrics on the numerical parameters are performed, achieving reductions in solution times by more than 60 percent with the full multigrid approach. Details of the circulation patterns are investigated in cavities of 2-to-1, 1-to-1, and 1-to-2 depth to width ratios.
Wood, William A.↗
Numerical studies of the fluid and optical fields associated with complex cavity flows
Numerical solutions for the flowfield about several cavity configurations have been computed using the Reynolds averaged Navier-Stokes equations. Comparisons between numerical and experimental results are made in two dimensions for free shear layers and a rectangular cavity, and in three dimensions for the transonic aero-window problem of the Stratospheric Observatory for Infrared Astronomy (SOFIA). Results show that dominant acoustic frequencies and magnitudes of the self excited resonant cavity flows compare well with the experiment. In addition, solution sensitivity to artificial dissipation and grid resolution levels are determined. Optical path distortion due to the flow field is modelled geometrically and is found to match the experiment. The fluid field was computed using a diagonalized scheme within an overset mesh framework. An existing code, OVERFLOW, was utilized with the additions of characteristic boundary condition and output routines required for reduction of the unsteady data. The newly developed code is directly applicable to a generalized three dimensional structured grid zone. Details are provided in a paper included in Appendix A.
Atwood, Christopher A.↗
Characterization of cavity flow fields using pressure data obtained in the Langley 0.3-Meter Transonic Cryogenic Tunnel
Static and fluctuating pressure distributions were obtained along the floor of a rectangular-box cavity in an experiment performed in the LaRC 0.3-Meter Transonic Cryogenic Tunnel. The cavity studied was 11.25 in. long and 2.50 in. wide with a variable height to obtain length-to-height ratios of 4.4, 6.7, 12.67, and 20.0. The data presented herein were obtained for yaw angles of 0 deg and 15 deg over a Mach number range from 0.2 to 0.9 at a Reynolds number of 30 x 10(exp 6) per ft with a boundary-layer thickness of approximately 0.5 in. The results indicated that open and transitional-open cavity flow supports tone generation at subsonic and transonic speeds at Mach numbers of 0.6 and above. Further, pressure fluctuations associated with acoustic tone generation can be sustained when static pressure distributions indicate that transitional-closed and closed flow fields exist in the cavity. Cavities that support tone generation at 0 deg yaw also supported tone generation at 15 deg yaw when the flow became transitional-closed. For the latter cases, a reduction in tone amplitude was observed. Both static and fluctuating pressure data must be considered when defining cavity flow fields, and the flow models need to be refined to accommodate steady and unsteady flows.
Tracy, M. B.↗
Numerical solution of a three-dimensional cubic cavity flow by using the Boltzmann equation
A three-dimensional cubic cavity flow has been analyzed for diatomic gases by using the Boltzmann equation with the Bhatnagar-Gross-Krook (B-G-K) model. The method of discrete ordinate was applied, and the diffuse reflection boundary condition was assumed. The results, which show a consistent trend toward the Navier-Stokes solution as the Knudson number is reduced, give us confidence to apply the method to a three-dimensional geometry for practical predictions of rarefied-flow characteristics. The CPU time and the main memory required for a three-dimensional geometry using this method seem reasonable.
Hwang, Danny P.↗
Pressure Gradient Effects on Hypersonic Cavity Flow Heating
The effect of a pressure gradient on the local heating disturbance of rectangular cavities tested at hypersonic freestream conditions has been globally assessed using the two-color phosphor thermography method. These experiments were conducted in the Langley 31-Inch Mach 10 Tunnel and were initiated in support of the Space Shuttle Return-To-Flight Program. Two blunted-nose test surface geometries were developed, including an expansion plate test surface with nearly constant negative pressure gradient and a flat plate surface with nearly zero pressure gradient. The test surface designs and flow characterizations were performed using two-dimensional laminar computational methods, while the experimental boundary layer state conditions were inferred using the measured heating distributions. Three-dimensional computational predictions of the entire model geometry were used as a check on the design process. Both open-flow and closed-flow cavities were tested on each test surface. The cavity design parameters and the test condition matrix were established using the computational predictions. Preliminary conclusions based on an analysis of only the cavity centerline data indicate that the presence of the pressure gradient did not alter the open cavity heating for laminar-entry/laminar-exit flows, but did raise the average floor heating for closed cavities. The results of these risk-reduction studies will be used to formulate a heating assessment of potential damage scenarios occurring during future Space Shuttle flights.
Everhart, Joel L.↗
Pressure Gradient Effects on Hypersonic Cavity Flow Heating
The effect of a pressure gradient on the local heating disturbance of rectangular cavities tested at hypersonic freestream conditions has been globally assessed using the two-color phosphor thermography method. These experiments were conducted in the Langley 31-Inch Mach 10 Tunnel and were initiated in support of the Space Shuttle Return-To-Flight Program. Two blunted-nose test surface geometries were developed, including an expansion plate test surface with nearly constant negative pressure gradient and a flat plate surface with nearly zero pressure gradient. The test surface designs and flow characterizations were performed using two-dimensional laminar computational methods, while the experimental boundary layer state conditions were inferred using the measured heating distributions. Three-dimensional computational predictions of the entire model geometry were used as a check on the design process. Both open-flow and closed-flow cavities were tested on each test surface. The cavity design parameters and the test condition matrix were established using the computational predictions. Preliminary conclusions based on an analysis of only the cavity centerline data indicate that the presence of the pressure gradient did not alter the open cavity heating for laminar-entry/laminar-exit flows, but did raise the average floor heating for closed cavities. The results of these risk-reduction studies will be used to formulate a heating assessment of potential damage scenarios occurring during future Space Shuttle flights.
Everhart, Joel L.↗
Selected computations of transonic cavity flows
An efficient diagonal scheme implemented in an overset mesh framework has permitted the analysis of geometrically complex cavity flows via the Reynolds averaged Navier-Stokes equations. Use of rapid hyperbolic and algebraic grid methods has allowed simple specification of critical turbulent regions with an algebraic turbulence model. Comparisons between numerical and experimental results are made in two dimensions for the following problems: a backward-facing step; a resonating cavity; and two quieted cavity configurations. In three-dimensions the flow about three early concepts of the stratospheric Observatory For Infrared Astronomy (SOFIA) are compared to wind-tunnel data. Shedding frequencies of resolved shear layer structures are compared against experiment for the quieted cavities. The results demonstrate the progress of computational assessment of configuration safety and performance.
Atwood, Christopher A.↗
Evaluation of a vortex model of turbulent cavity flow
A two dimensional discrete vortex model is applied to turbulent flow over a cavity at a Reynolds number based on cavity half length of approximately 500,000. These model predictions are compared with experimental data on a time average and on a spectral basis. The comparisons indicate that the vortex model reproduces the mean velocity profiles of this complex flow, while the turbulent intensity and Reynolds stress profiles are overpredicted in magnitude. Spectral analyses show that the vortex model introduces unrealistic low frequency power which becomes less dominant as the model becomes more disordered. The spectral power distribution of the model in this state is nearly in agreement with that of the data, somewhat too low at the higher frequencies and too high at the lower frequencies. The model is shown to be capable of reproducing the cavity feedback oscillation phenomenon.
Hardin, J. C.↗
Effect of Sweep on Cavity Flow Fields at Subsonic and Transonic Speeds
An experimental investigation was conducted in the NASA Langley 7 x 10-Foot High Speed Tunnel (HST) to study the effect of leading- and trailing-edge sweep on cavity flow fields for a range of cavity length-to-height (l/h) ratios. The free-stream Mach number was varied from 0.2 to 0.8. The cavity had a depth of 0.5 inches, a width of 2.5 inches, and a maximum length of 12.0 inches. The leading- and trailing-edge sweep was adjusted using block inserts to achieve leading edge sweep angles of 65 deg, 55 deg, 45 deg, 35 deg, and 0 deg. The fore and aft cavity walls were always parallel. The aft wall of the cavity was remotely positioned to achieve a range of length-to-depth ratios. Fluctuating- and static-pressure data were obtained on the floor of the cavity. The fluctuating pressure data were used to determine whether or not resonance occurred in the cavity rather than to provide a characterization of the fluctuating pressure field. Qualitative surface flow visualization was obtained using a technique in which colored water was introduced into the model through static-pressure orifices. A complete tabulation of the mean static-pressure data for the swept leading edge cavities is included.
Tracy, Maureen B.↗
CSCM methodology for slot injection cooled cavity flow design in a high enthalpic stream
The CSCM method for the compressible Navier-Stokes equations is applied to study design factors in a slot injection cooled cavity flow in the side of a 2-D wedge body in a high enthalpy free stream. The flow geometry is being designed and will be tested in an arc jet tunnel at NASA-Ames Research Center. Objectives of the design are to provide adequate thermal protection for and minimize aero-optical distortion in the path above a window located in the bottom of the cavity. Among design issues, are the geometry of and flow conditions in the expanding section of the supersonic slot injection nozzle. Here, for straight walled nozzles, two geometries are considered for the upper nozzle lip between the hot, high speed outer flow and the colder, denser cooling flow. The two lip geometries - thick, square and thin, wedge - as the result of associated widely differing base/wake flows also exhibit different and interesting viscous-inviscid flow structures near the ramp termination to the cavity. For the thin lip case, the consequences on flow quality of off design nozzle conditions relative to matching pressure with the outer flow are explored.
Bardina, Jorge↗