Cavities

Cavity Description

The rotating cavity solver is used to calculate the fluid rotational velocity and temperature change in control volumes bounded by rotating (and stationary) surfaces. Cavities are commonly needed to model the secondary flows (flow not in the main gas path) of turbo machinery applications. The solver uses an angular momentum balance between the flow entering and leaving the control volume and the torque applied to the flow by the rotating and stationary surfaces. The rotating fluid leads to a pressure gradient in the radial direction. The rotating velocity (swirl) of the fluid is used by the vortex elements to introduce the pressure gradient into the flow model. The temperature change due to the cavity is automatically applied to the flow.

Quick Guide for Creating a Cavity in the GUI

  1. Right-click on a vortex chamber or inertial chamber (a cavity cannot be applied to a plenum or momentum chamber) and select Create Cavity. An optional cavity title can be given to help identify it.


    Figure 1.
  2. Create the surfaces of the cavity. Cavities usually have multiple surfaces, with each surface associated with a different part in the machine. Each surface must have a unique speed so do not use points from a rotating and stationary part on the same cavity surface. Cavity surface points can be created using 1)the traditional approach of selecting a point on the screen close to the CAD geometry or 2) using the CAD geometry to place points directly on the curves.
  3. The Create option works best for creating a new surface with the traditional approach. Use the Insert, Move, and Delete options to edit an existing surface. Select the surface points on the screen to fully define the cavity surface.


    Figure 2.
  4. Create surface points directly on the CAD geometry one at a time.


    Figure 3.
  5. Create multiple surface points directly on the CAD geometry with one click.


    Figure 4.
  6. You can modify the friction options for the surface if needed. Bolt rows or other features that affect the surface drag can be included.
  7. After the surfaces are created, the flows entering and exiting the control volume must be defined. The Auto Fill button can be used to populate the table. However, “Auto Fill” must have information from completed elements to work properly, so complete input for elements that are attached to the cavity chamber before attempting “Auto Fill”. Manual edits to this table may be required. The three inputs for each flow include:
    1. Radius: The radius (inches) of the flow entering or exiting the cavity control volume.
    2. Swirl Source: The chamber containing the swirl of the flow entering the cavity. Enter a “0” if the swirl of the fluid exiting the Flow Element is to be used (needed if no chamber contains the proper swirl). The Swirl Source for Outflows will only be used by the solver if the flow reverses in the element.
    3. Flow Element: The number of the flow entering or exiting the cavity control volume.


    Figure 5.
  8. Use the Cavity section in the Flow Model Browser to adjust the cavity display and to delete cavities if needed. The Colour by surface rotor speed is useful for visualizing the surface speeds (Blue = stationary and Red = Rotor 1). Left-click twice on a cavity in the list to center the view on the cavity. The User Settings panel has the surface point size control as a percentage of the chamber/element symbol size.


    Figure 6.

Cavity Inputs

The Flow Simulator cavity solver input data consists of four separate name list blocks near the bottom of the model database file. The first of these, $CAV1, defines the number of separate cavities to be analysed and is used to set any global input variables that are related to cavities. Each cavity requires a $CAV name list block and a $FLOWCAV name list block. Both $CAV and $FLOWCAV define cavity variables with the $FLOWCAV variables providing information about flow, swirl, pressure, and temperature connectivity between the cavity and chambers in the model. Each $CAV name list block contains NSURF, which identifies the number of surfaces in the cavity or sub-cavity. NSURF is the number of sets of $SURF name list blocks that are required for the cavity or sub-cavity since the $SURF name list block provides details about cavities surfaces. The following listing contains a description of the cavity inputs for each of the name list blocks. All required name list variables have been highlighted.

Namelist Variable Description
$CAV1 Cavity Solution Tolerance

(TOLCV)

Cavity solution tolerance for net wall torque / angular momentum change.

(Default value = 1.0E-04)

$CAV1 Max Cavity Interval

(MAX_CAV_INTERVAL)

Maximum number of Flow Simulator solver iterations between cavity solver runs. If the limit is reach, the cavity solver is forced to run.

(Default value = 50)

$CAV1 Max Global Cavity Run

(MAX_FLOBAL_CAV_RUN)

Maximum number of times cavity will run after flow balance is achieved before giving up.

(Default value = 10)

$CAV1 Max Cavity Runs

(MAX_CAVITY_RUNS)

Maximum number of cavity solver runs.

(Default value = 99999)

$CAV1 Cavity First Run Iteration Limit

(CAV_FIRST_RUN_ITER_LIMIT)

Number of iterations at the start when CAV_FIRST_RUN_ERR_LIMIT applies.

(Default value = 50)

$CAV1 Cavity First Run Error Limit

(CAV_FIRST_RUN_ERR_LIMIT)

Maximum flow balance error to trigger a cavity run.

Used when number of Flow Simulator iterations is less than or equal to CAV_FIRST_RUN_ITER_LIMIT.

(Default value = 100%)

$CAV1 Cavity Run Sec. Limit Factor

(CAV_RUN_SEC_LIMIT_FACTOR)

Maximum flow balance error to trigger a cavity run.

Used when the number of Flow Simulator iterations is greater than CAV_FIRST_RUN_ITER_LIMIT.

(Default value = 2.5%)

$CAV1 Swirl Change Tolerance

(XK_CHANGE_TOL)

Tolerance for swirl change between cavity runs.

If swirl change is greater than XK_CHANGE_TOL, then Flow Simulator will continue running.

(Default value = 0.02)

$CAV1 Global Cavity Run Limit

(FLOBAL_CAV_RUN_LIMIT)

Value of maximum error (cavity chamber flow balance) allowed above which the individual cavity is not run.

(Default value = 50.0%)

$CAV1 Torque Integration Method

(TRQINTG)

Cavity torque integration method.

(Default value = 1)

$CAV1 Max Iterations

(MAX_ITER)

Maximum number of iterations for cavity solver convergence.

(Default value = 200)

$CAV1 Cavity Surface Tolerance

(SURTOL)

Tolerance value to define a surface segment as either horizontal or vertical (in).

(Default value = 0.0012)

$CAV1 SURFTREAT Cavity surface treatment flag. Method used to determine if a surface segment is cylindrical or conical/vertical.

This flag is not available in or written by the GUI. Internally, Flow Simulator interprets this flag based on the value of TRQINTG as shown below.

$CAV1 CF_DISK_ROTOR

CF_DISK_STATR

CF_CYLR_ROTOR

CF_CYLR_STATR

The global cavity surface friction option. These options are used on all cavity surfaces that do not have a local cavity surface friction option specified.

-1: User Specified Friction Factor

0: Use default friction correlations

5: Disk Friction Factor from Dasoghe reference

11: Disk Friction Factor from Sultanian reference

12: Cylinder Friction Factor from Sultanian reference

>1000: Custom friction factor correlation

Namelist Variable Description
$CAV NSURF Number of cavity surfaces.

(Mandatory Input)

$CAV Title (TITLE) Title for cavity, which can contain up to 70 characters.
$CAV CH

(NCHAMB)

Chamber identification number of the chamber that stores the swirl factor and rotor index used by this cavity.

NCHAMB serves as the cavity identifier

(Mandatory Input)

$CAV ACTIVE_CAV

[checkbox]

Flag that indicates whether or not this cavity should be solved.

Can be turned on/off using the checkbox in the Flow Simulator cavity window.

If ACTIVE_CAV is 0, this is equivalent to removing the cavity from the model.

(Default value = 1)

$CAV ICSOL Cavity windage calculation method.

0: Single outflow method: windage computed for rotor drag.

1: Multiple outflow method: windage computed for stator drag and pumping.

(Default value = 1 = MULTIPLE_OUT)

$CAV DTLIM Maximum temperature rise (F) due to windage.

(Default value = 500 F)

$CAV CF_DISK_ROTOR

CF_DISK_STATR

CF_CYLR_ROTOR

CF_CYLR_STATR

The local cavity surface friction option. These options are used for the current cavity surfaces. If set to 0, the global options are used.
$SURF Surface Speed

(IXN)

Surface rotation pointer (to ELERPM array from general data). A value of 0 indicates the surface is stationary.

(Mandatory Input)

$SURF X Axial position

(Mandatory Input)

$SURF R Radial position

(Mandatory Input)

$SURF Number of Bolt Rows

(NBROW)

Number of bolt rows.

(Default value = 0)

$SURF Number of bolts

(NB)

Number of bolts for each row.

(Used only when NBROW > 0)

$SURF Bolt circle radius

(RB)

Bolt circle radius (in) for each bolt row.

(Used only when NBROW > 0)

$SURF Bolt diameter

(DB)

Bolt diameter (in) for each bolt row.

(Used only when NBROW > 0)

$SURF Bolt height

(HB)

Bolt height (in) above surface for each bolt row.

(Used only when NBROW > 0)

$SURF Bolt drag coefficient

(CDB)

CD for each bolt row (spacing correction is automatic).

(Used only when NBROW > 0)

$SURF Surface Roughness

(CDO1)

CD flag for hooks or H/C multipliers, etc.

0: Smooth wall (no multiplier of additional roughness)

> 0: Horner shape factor

< 0: Surface multiplier (program uses absolute value)

(Default value = 0.)

$SURF Protrusion Pitch

(XP1)

Distance (in) between protrusions.

(Only used if CDO1 > 0.)

$SURF Protrusion Height

(H1)

Height (in) of protrusion.

(Only used if CDO1 > 0.)

$SURF FR1 User supplied friction factor to be used instead of the calculated value.
$SURF FORCE_DIR The axial direction of the pressure force on this cavity surface. The pressure force and force direction will be used during post processing to sum axial forces on cavity surfaces.

-1: pressure force acts in negative axial direction

0: no pressure force for this surface

1: pressure force acts in positive axial direction

$SURF HT Heat Transfer option for this surface

0: no heat transfer on this surface

1: apply heat transfer to this surface

$SURF TSURF The cavity surface temperature for heat transfer. (deg F)
$SURF HTC_REL The Heat Transfer Coefficient relation.

-1: Constant HTC

>1000: Use a custom HTC correlation, ROTATING_CAVITY_NU custom subtype.

$SURF HTC The Heat Transfer Coefficient when HTC_REL=-1, BTU/(hr ft^2 F)
$FLOWCAV CH Pressure ID

(P)

Chamber identification number where cavity pressure is stored and retrieved. If left unset, Flow Simulator will use NCHAMB.

(Default value = cavity NCHAMB)

$FLOWCAV CH Temp. ID

(TIN)

Chamber identification number where cavity temperature is stored and retrieved. If left unset, Flow Simulator will use NCHAMB.

(Default value = cavity NCHAMB)

$FLOWCAV FS Secondary fluid mass fraction of entering flow or pointer to Flow Simulator chamber or element (optional).

(Default value = cavity NCHAMB)

$FLOWCAV RIN1 Radius (in) to flows entering the cavity from the engine centerline.

(One value required for each WIN.)

(Mandatory Input)

$FLOWCAV ROUT1 Radius (in) to flows leaving the cavity from the engine centerline.

(One value required for each WOUT.)

(Mandatory Input)

$FLOWCAV XNW Source of swirl for flows entering the cavity.

CHNUM: Use swirl from chamber CHNUM.

0: Use swirl from the element exit.

(There must be an XNW entry for each WIN and WOUT entry in case flow reverses. The entries that correspond to WOUT are used when flow reverses.)

(Mandatory Input)

$FLOWCAV WIN Element identification number of elements that are expected to have flows entering the cavity.

(Mandatory Input)

$FLOWCAV WOUT Element identification number of elements that are expected to have flows leaving the cavity.

(Mandatory Input)

Cavity Theory Manual

The fluid rotational speed in the cavity is computed based on inlet velocities, mass flows, and computed surface torque. The surface torque and cavity swirl factor are interdependent. The cavity solver carries out an iterative procedure to ensure both sets of equations are satisfied. In particular, the Regula Falsi method is employed with the initial guess for cavity swirl to iteratively seek the correct cavity swirl value that satisfies the angular momentum equation within the specified tolerance. For the first call to the cavity solver, the initial guess is based on the user’s entry from upstream chamber swirl (or downstream chamber swirl if flows are reversed). For subsequent cavity runs, the initial guess is based on the previous cavity analysis result. The calculated cavity swirl is representative of the cavity fluid control volume and is used as the cavity exit swirl.

In Flow Simulator, vortices and cavities follow the chamber-centric modelling approach. Cavities can be modelled with multiple inflows and outflows. This section presents the physical equations that govern the cavity vortex as implemented in Flow Simulator. The feature that distinguishes the cavity vortex from free and forced vortexes is its calculation of torque caused by the rotating metal parts acting on the fluid passing through the cavity. Torque affects fluid velocity, temperature, and pressure in the cavity, which are subsequently calculated by including the torque term in the momentum and energy balance equations.

The Angular Momentum equation

Nomenclature:

KE: Volumetric Kinetic Energy

ρ: Fluid density

r, R: Radius from the engine centreline

Ω: Rotational speed

N: Speed in terms Rotation per Minute

XK: Ratio of the fluid absolute rotational speed to the rotational reference frame (i.e. rotor)

τ: Torque

cf: Coefficient of friction

x: Axial location of surface segment endpoint

α: Angle that the surface makes with the engine centreline

Nb: Number of bolts in the bolt row

Cdb: Cd for the bolt row (spacing correction is automatic)

Sb: Bolt interference scale factor for the bolt row

Ab: Cross sectional area of exposed bolt head surface

Rb: Radius from the engine centerline the bolt row

k: Cavity surface index

csf: Cylindrical surface skin friction

nsf: Non-cylindrical surface skin friction

CAV: Cavity control volume

ref: Cavity rotational reference frame

s: Cavity surface segment index

1,2: Cavity surface segment endpoints

i, j: Cavity inflow/outflow element indexes

const: Indicates that any radius terms have been removed from the parameter, this is useful to allow parameters to be pulled outside of an integral taken with respect to radius as “constants”

Surface Skin Friction Torque:

Torque due to non-cylindrical surfaces (Conical, Vertical surfaces with respect to engine centreline) and Cylindrical surfaces (Horizontal surfaces with respect to engine centreline) is computed either by a numerical integral or by the exact integral method. The torque integration method option is available under SolveràAnalysis SetupàSolver ConvergenceàCavity Solver Tolerancesà Torque integration method dropdown menu. The torque coefficients equations are summarized under following table:

The Volumetric kinetic energy term is defined as

Surface Bolts Form Drag Torque

Torque equation for bolts can be found in Sultanian (ref 6), section 4.3.2.

The interference scale factor, Sb,k,r is based on Fig 30 on page 5-14 of Hoerner (ref 7).

The skin friction coefficient equation depends on whether the surface is stationary or rotating. The following table presents the skin friction coefficient equations

The relation for friction coefficients on non-cylindrical surfaces that is used in all the cavity solvers was developed from data for rotating disks. Since most of the non-cylindrical surfaces in the cavities of interest are annuli rather than complete disks, use of an average radius was selected as the preferable method for the Flow Simulator cavity solver. As verified by running a wide range of test cases, the variation in results due to these methodological differences are generally minor and well within the range of engineering accuracy for the analysis.

Delta Temperature across cavity:

The temperature rise across the cavity is calculated using energy balance accounting for the windage generated by rotor. The Energy balance and Delta Temperature Rise calculation are as follows:

Single In/Outflow Cavity:

Multiple In/Outflow Cavity

Cavity Heat Transfer

In addition to the fluid temperature change due to windage, the fluid temperature can also change due to the fluid convection to the cavity surface. The typical convection heat transfer equation is used:
q convection =HTC*Area* T surf T fluid rel MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGXbWdamaaBaaaleaapeGaam4yaiaad+gacaWGUbGaamODaiaa dwgacaWGJbGaamiDaiaadMgacaWGVbGaamOBaaWdaeqaaOWdbiabg2 da9iaadIeacaWGubGaam4qaiaacQcacaWGbbGaamOCaiaadwgacaWG HbGaaiOkamaabmaapaqaa8qacaWGubWdamaaBaaaleaapeGaam4Cai aadwhacaWGYbGaamOzaaWdaeqaaOWdbiabgkHiTiaadsfapaWaaSba aSqaa8qacaWGMbGaamiBaiaadwhacaWGPbGaamizaiaacckacaWGYb GaamyzaiaadYgaa8aabeaaaOWdbiaawIcacaGLPaaaaaa@5AEB@

HTC = Heat transfer coefficient (user-supplied) or calculated by the correlation.

Area = Surface area

Tsurf = The surface temperature (user-supplied).

Tfluid rel = The relative fluid total temperature, adjusted for fluid and surface rotation.

Cavity Pressure

The cavity pressure is simply the pressure that Flow Simulator has assigned to the cavity chamber. If the cavity chamber is an inertial chamber the pressure is calculated during the normal network solution process. If the cavity chamber is a vortex chamber, the pressure comes from the vortex element segment that uses this vortex chamber. The pressure is only used in the cavity solver to determine the fluid properties. The pressure ratio across a cavity can only be calculated using a vortex element.

Cavity Surface Axial Force

The cavity surface axial force is calculated as:
Forc e surf =Forc e dir *Area* P chamber MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbGaam4BaiaadkhacaWGJbGaamyza8aadaWgaaWcbaWdbiaa dohacaWG1bGaamOCaiaadAgaa8aabeaak8qacqGH9aqpcaWGgbGaam 4BaiaadkhacaWGJbGaamyza8aadaWgaaWcbaWdbiaadsgacaWGPbGa amOCaaWdaeqaaOWdbiaacQcacaWGbbGaamOCaiaadwgacaWGHbGaai OkaiaadcfapaWaaSbaaSqaa8qacaWGJbGaamiAaiaadggacaWGTbGa amOyaiaadwgacaWGYbaapaqabaaaaa@5441@

Forcedir=Force direction (user-supplied) for this surface, either -1 or 1.

Pchamber=Static pressure of the cavity chamber.

Area = Surface area for this cavity surface, Area=π*abs radiu s 1 2 radiu s n 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGbbGaamOCaiaadwgacaWGHbGaeyypa0JaeqiWdaNaaiOkaiaa dggacaWGIbGaam4Camaabmaapaqaa8qacaWGYbGaamyyaiaadsgaca WGPbGaamyDaiaadohapaWaa0baaSqaa8qacaaIXaaapaqaa8qacaaI YaaaaOGaeyOeI0IaamOCaiaadggacaWGKbGaamyAaiaadwhacaWGZb WdamaaDaaaleaapeGaamOBaaWdaeaapeGaaGOmaaaaaOGaayjkaiaa wMcaaaaa@51C8@ .

Radius1 = Radius of first point of cavity surface.

Radiusn = Radius of the last point of the cavity surface.

The cavity forces are summed for all cavities using the surface rotation and written to the *.cav.out file. For example, all forces are summed for the surface rotating with rotor 1 RPM.

Cavity Outputs

The following listing provides details about cavity output variables. The first table shows the cavity output variables in the summary section. The second table shows the cavity output variables in the detailed (individual) cavity results.

NAME DESCRIPTION UNITS

ENG, SI

NCHAMB Cavity identification number, also the number of the associated chamber. (ID)
XK Ratio of the absolute rotational speed of the fluid to the reference frame rotational speed (REF_RPM). (unitless)
WINDAGE Heat added due to cavity windage.

For the new multiple outflow cavity methodology, this is the sum of the stator windage and rotor pumping for element flow(s) exiting the cavity.

BTU/s, W
DT_WNDG Total absolute temperature rise due to windage.

For the new multiple outflow cavity methodology, this is the sum of the stator windage and rotor pumping for element flow(s) exiting the cavity.

deg F, K
TEMPERATURE Total absolute temperature in the cavity, also stored as TTC of cavity chamber (NCHAMB).

For the new multiple outflow cavity methodology, this temperature only includes the effect from the stator windage and rotor pumping for all element flows entering the cavity. The change in temperature due to rotor pumping for any flow(s) exiting the cavity is applied to the chamber(s) downstream of the element(s).

deg F, K
PRESSURE Static pressure in the cavity, also stored as PSC of cavity chamber (NCHAMB). Psia, mPa
FL2_MASS_FRAC Secondary fluid mass fraction, also stored as FS of the cavity chamber (NCHAMB). (unitless)
CONV_ITER Number of iterations required for the cavity to converge on the most recently completed cavity run. (number)
REF_RPM Reference rotational speed for the cavity.

Used with swirl factor (XK) to calculate fluid rotational speed

rev/min
NAME DESCRIPTION UNITS

ENG, SI

CAVITY CHAMBER Cavity identification number, also the number of the associated chamber. (ID)
CAVITY SOLVER

ITERATIONS

Number of iterations required for the cavity to converge on the most recently completed cavity run. (number)
REF RPM Reference rotational speed for the cavity.

Used with swirl factor (XK) to calculate fluid rotational speed

rev/min
CAVITY XK Ratio of the absolute rotational speed of the fluid to the reference frame rotational speed (REF RPM). (unitless)
CAVITY FLUID RPM Rotational speed of the fluid in the cavity rev/min
CHAMBER TEMPERATURE Total absolute temperature in the cavity, also stored as TTC of cavity chamber.

For the new multiple outflow cavity methodology, this temperature only includes the effect from the stator windage and rotor pumping for all element flows entering the cavity. The change in temperature due to rotor pumping for any flow(s) exiting the cavity is applied to the chamber(s) downstream of the element(s).

deg F, K
CONVERGENCE

STATUS

Cavity convergence status (flag)
CAVITY WINDAGE

METHOD

Cavity windage calculation method

TOTAL APPLIED TO CAVITY

All cavity results are applied to the cavity chamber. This is used for single outflow cavities (ICSOL = 0).

MULTIPLE OUTFLOW, PUMPING APPLIED TO FLOW

Stator windage and rotor pumping for flow(s) entering the cavity are applied to the cavity chamber. Rotor pumping for flow(s) exiting the cavity is applied to the chamber(s) downstream of the element(s). This is used for multiple outflow cavities (ICSOL = 1).

(flag)
ROTOR_WINDAGE

(STATOR + PUMP

WINDAGE)

Heat added in the cavity due to windage (friction and drag) and rotor pumping of the fluid. BTU/s, W
T RISE FROM

ROTOR WINDAGE

(T RISE FROM STATOR +

PUMP WINDAGE)

Temperature rise due to cavity windage and rotor pumping. deg F, K
SECOND FLUID MASS

FRACTION

Secondary fluid mass fraction, also stored as FS of the cavity chamber (NCHAMB). (unitless)
PRESSURE Static pressure in the cavity, also stored as PSC of cavity chamber (NCHAMB). psia, mPa
SURFACE Cavity surface index. (index)
SURFACE_RPM Rotational speed of each cavity surface rev/min
TOTAL_TORQUE Total torque applied to the fluid by each surface. ft*lbf, N-m
GEOM_PARAM An intermediate variable that gathers geometric data for cylindrical segments and non-cylindrical segments of each surface and is then used to compute surface torque. ft5, m5
RADIUS Effective radius of each cavity surface. inch, m
COEFF_FRIC Effective skin friction coefficient of each surface. (unitless)
RE Fluid Reynolds number for each surface. inch, m
SURF_WINDAGE_Q Windage due to each surface. BTU/s, W
SURF_WINDAGE_DT Temperature rise due to windage from each surface. deg F, K
ELEMENT Element identification number for each cavity inflow and outflow. (ID)
ANG_MOM Angular momentum due to each flow into and out of the cavity. ft*lbf, N-m
FLOW Flow rate of each cavity inflow and outflow. lbm/s, kg/s
XK_SRC Source of fluid swirl factor for each cavity inflow.

CH: Fluid swirl factor for the flow is obtained from specified chamber.

EL: Fluid swirl factor for the flow is obtained from specified element.

(ID)
XKIN Swirl factor of each cavity inflow. (unitless)
RPM_REF Reference rotational speed for each cavity inflow.

Used with swirl factor (XK) to calculate fluid rotational speed

rev/min
PUMP_Q Rotor pumping (heat) for each flow into and out of the cavity.

Only printed when using MULTIPLE OUTFLOW, PUMPING APPLIED TO FLOW (ICSOL = 1) cavity method.

BTU/s, W
PUMP_DT Change in fluid temperature due to rotor pumping for each flow into and out of the cavity.

Only printed when using MULTIPLE OUTFLOW, PUMPING APPLIED TO FLOW (ICSOL = 1) cavity method.

deg F, K
PUMP_CH Identification number of the chamber to which the rotor pumping (heat) is applied to for each flow into and out of the cavity.

For flow(s) into the cavity, the heat is applied to the cavity chamber. For flow(s) exiting the cavity, the heat is applied to the chamber(s) downstream of the element(s).

Only printed when using MULTIPLE OUTFLOW, PUMPING APPLIED TO FLOW (ICSOL = 1) cavity method.

(ID)

References

  1. Da Soghe, R., Facchini, B., Innocenti L. and Micio, M., Analysis of Gas Turbine Rotating Cavities by a One-Dimensional Model: Definition of New Disk Friction Coefficient Correlations Set, ASME Journal of Turbomachinery, Vol 133, 2011.
  2. Da Soghe, R., Innocenti L., Andreini A., and Poncet, S., Numerical benchmark of turbulence modeling in gas turbine rotor-stator system, ASME Turbo Expo 2010, GT2010-22627, 2010.
  3. Da Soghe, R., Facchini, B., Innocenti L. and Micio, M., Some Improvements in a Gas Turbine Stator-Rotor Systems Core-Swirl Ratio Correlation, International Journal of Rotating Machinery, Volume 2012, Article ID 853767, 2012.
  4. Owen, J.M. and Pincombe, J.R., Velocity measurements inside a rotating cylindrical cavity with a radial outflow of fluid, Journal of Fluid Mechanics, Vol. 99(1), pages 111 – 127, 1980.
  5. Owen, J.M., Pincombe, J.R. and Rogers R. H., Source-sink flow inside a rotating cylindrical cavity, Journal of Fluid Mechanics, Vol. 155(1), pages 233 – 265, 1985.
  6. Bijay K. Sultanian, “Gas Turbines – Internal Flow Systems Modeling”, Cambridge Aerospace series, 2018, ISBN 978-1-107-17009-4
  7. Hoerner, S. F., “Fluid-Dynamic Drag”, 1965, Author-Published