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BLEED - Bleed region flow rate

Structured Grids

BLEED {MASS region mdot | POROSITY region pplen por [dis] | \
       EMPIRICAL region mode blv1 blv2 blv3 blv4 | \
       FORCING region amp freq phase | WALL region [TEMPERATURE temp] | \
       AEDC region dstar por aspect}

Unstructured Grids

BLEED {MASS region mdot | POROSITY region pplen por dis | \
       FORCING region amp freq phase | WALL region} [TEMPERATURE temp]

The effect of bleed on the flow can be modeled, if bleed regions were identified in the grid file. The parameters discussed below identify the bleed rate for each region, for a specific solution. If a bleed region is not named in this file, its bleed rate is set to zero.

There are several possible bleed modes available. Unless noted otherwise, the keywords apply to both structured and unstructured grids.

Bleed is only allowed for perfect gases, for both structured and unstructured grids. With unstructured grids, the bleed boundary condition is applied at the cell faces, but the flow field values written to the .cfl file for post-processing are at the nodes. The results may thus be slightly different around the edges of the bleed region with structured and unstructured grids.

BLEED MASS region mdot

    region   Bleed region number from .cgd file
mdot Normalized bleed flow rate

mdot can also be thought of as the mass flow ratio for the bleed region. The actual bleed mass flow is calculated as

mbleed = mdot * (ρUAc)

where Ac is an arbitrarily set reference "capture area" that you must specify, in either GMAN (using the CAPTURE AREA command, or the BOUNDARY COND. menu) or MADCAP (using Set Capture Area from the Boundary Conditions menu), in each zone of the grid file that contains bleed areas.

The bleed velocity will automatically be limited to Mach 1.

Although this is intended as a bleed model, it can also be used for blowing by setting mdot to a negative value.

BLEED POROSITY region pplen por dis

[There are some questions about the coding for the porous bleed model that need to be resolved. This model should be therefore used with caution.]

    region   Bleed region number from .cgd file
pplen Back pressure pplen, in psia
por Porosity
dis Discharge coefficient; may be defaulted for structured grids

With this model, the velocity at the wall will be computed from the local pressure p in the flow field, and the specified back pressure pplen. If p > pplen, the flow will be out of the computational domain (i.e., bleed). If p < pplen, the flow will be into the computational domain (i.e., blowing).

For unstructured grids, the discharge coefficient must be specified. For structured grids, however, it may be omitted. In this case, for bleed a default value is computed from the specified back pressure and the local flow conditions, using the empirically-based method of Dittrich and Graves [Dittrich, Ralph T., and Graves, Charles C. (1956) "Discharge Coefficients for Combustor-Liner Air-Entry Holes", NACA TN 3663]. For blowing, the default value for the discharge coefficient is 0.6.

BLEED EMPIRICAL region mode blv1 blv2 blv3 blv4

This keyword specifies use of an empirical bleed model that allows the bleed mass flow rate to vary in response to local flow conditions. The input parameter region is the bleed region number from the .cgd file. The input data for the bleed model is given by the values of blv1 through blv4. Various combinations of values may be specified, depending on the mode, as described below. Modes 1, 2 and 8 are only available for structured grids.

    mode   blv1   blv2   blv3   blv4   Description
1 pplen Porosity qsmode Nbl Mayer-Paynter model with boundary layer edge specified.
2 pplen Porosity qsmode Mayer-Paynter model with boundary layer edge assumed at the grid index midpoint.
3 pplen Porosity qsmode M Mayer-Paynter model with boundary layer edge Mach number specified.
4 Qsonic Porosity M Mayer-Paynter model with Qsonic and edge Mach number specified
5 pplen Porosity Slater model with specified plenum pressure.
6 pexit Porosity Cdis Aexit Slater model with fixed bleed plenum exit area and pressure.
7 pplen Porosity mbleed Slater model with specified mass flux.
8 pplen Porosity Aexit Nbl Bunnag model. (Under development)

The input parameters are illustrated in the figure below and can be described as follows: Aexit is the bleed exit area, Cdis is the bleed exit discharge coefficient, M is the local Mach number at the edge of the boundary layer, mbleed is the actual bleed flow rate, Nbl is the number of grid points in the boundary layer, Qsonic is the sonic mass flow coefficient (described below), pexit is the bleed exit static pressure, and pplen is the bleed plenum static pressure.

Schematic of bleed boundary
Schematic of bleed boundary

The parameter qsmode is an integer defining how Qsonic is to be computed.

    qsmode   Meaning
    1   Set Qsonic = 1
2 Compute Qsonic for 90° holes
3 Compute Qsonic for 20° holes
4 Compute Qsonic for 90° holes using the Qsonic-B formulation

Mayer-Paynter Model

In the Mayer-Paynter model [Mayer, D. W. and Paynter, G. C. (1994) "Boundary Conditions for Unsteady Supersonic Inlet Analyses," AIAA Journal, Vol. 32, No. 6, pp. 1200-1206], the bleed flow rate is determined from local solution values at the edge of the boundary layer.

Given the local boundary layer edge Mach number, the freestream total conditions are approximated from the local boundary wall values (B).

pTpB [ 1 + 0.5*(γ−1)*M2 ]γ/(γ−1)

The actual mass flow rate through the bleed holes is calculated from

mbleed = msonic Qsonic

where msonic is the ideal maximum flow rate (based on the local freestream total pressure and temperature) that would occur through the bleed holes at sonic conditions

msonic = φ AB G pT ( γ / R TT )1/2

Porosity (φ) is defined as the ratio of the bleed hole area to the boundary surface area, and G is simply a function of the specific heat ratio.
φ = Ableed / AB
G = [1 + (γ−1)/2] −[(γ+1)/2(γ−1)]

Lastly, Qsonic is the sonic mass flow coefficient.
Qsonic = f (α, M, pplen/pT )

Qsonic is a function of the bleed hole angle α, the local Mach number M, and the ratio of the plenum pressure pplen to the local total pressure pT. The functional relationship is in the form of tabulated experimental data for circular bleed holes at angles of 20° and 90°. The 20° data were taken by McLafferty and Ranard [McLafferty, G., and Ranard, E. (1958) "Pressure Losses and Flow Coefficients of Slanted Perforations Discharging from Within a Simulated Supersonic Inlet," United Aircraft Corporation, Report R-0920-1, Dec. 1958], and the 90° data were taken by Syberg and Hickox [Syberg, J. and Hickox, T. E. (1972) "Design of a Bleed System for a Mach 3.5 Inlet," NASA CR-2187, Sept. 1972]. The data are contained in the figure below.

Qsonic Flow Coefficient Data
Sonic flow coefficient data for 20° and 90° bleed holes [See Mayer and Paynter (1994)].

Using the relations above, the local average wall bleed velocity can be computed from

vB = mbleed / ρB AB = Qsonic φ G TB (γ R / TT)1/2 (pT/pB)

Slater Model

In the Slater model [Slater, J. W., "Improvements in Modeling 90° Bleed Holes for Supersonic Inlets," NASA TM-2009-215597 / AIAA Paper 2009-0710, June 2009], the bleed flow rate is determined from local solution values at the bleed boundary surface (B). This is accomplished by rescaling the terms used in the Mayer-Paynter model to remove the freestream Mach number sensitivity.

The actual mass flow rate through the bleed holes is calculated from

mbleed = msonic-B Qsonic-B

msonic-Bmsonic [ pB/pT (TT/TB )1/2 ] = φ AB G pB (γ R TB)1/2
Qsonic-BQsonic [ pB/pT (TT/TB)1/2 ]-1
Qsonic-B is referred to as the surface sonic mass flow coefficient. As shown in the figure below, it is not as sensitive as Qsonic to the local freestream Mach number and is therefore approximated using a single curve fit to the 90° bleed hole data of Willis, Davis, and Hingst [Willis, B. P., Davis, D. O., and Hingst, W. R. (1995), "Flow Coefficient Behavior for Boundary Layer Bleed Holes and Slots," AIAA Paper 95-0031.]
Qsonic-B = f ( α, pplen/pB )

Original and Surface Qsonic Scaling
Original and surface sonic flow coefficient data for 90° bleed holes [See Slater (2009)].

Using these relations, the local average wall bleed velocity can be computed from

vB = mbleed / ρB AB = Qsonic-B φ G (γ R TB)1/2

For qsmode=6, the plenum pressure is not prescribed. Instead, it is determined assuming a fixed bleed plenum exit area and pressure. The bleed flow rate must match that at the bleed exit, which is computed from an ideal flow rate and the prescribed discharge coefficient.

Pplen / Pexit = [1+0.5*(γ−1)*M2exit] γ/(&gamma−1)
mexit = Cdis Pplen Aexit Mexit ( γ / R Tplen)1/2 [ 1 + 0.5*(γ−1)*M2exit ] &minus(γ+1)/2(γ−1)

Assuming that TplenTB, one can iterate the plenum pressure and compute the above quantities (Mexit , mexit , Qsonic-B , msonic-B , and mbleed) until the criteria mbleedmexit is met. Once the bleed flow rate is known, the wall velocity can be computed.

For qsmode=7, an initial plenum pressure is prescribed. After that, the plenum pressure is adjusted until mbleed meets the prescribed mass flow rate. A positive flow rate means that fluid is exiting the domain.

BLEED FORCING region amp freq phase

This mode allows an oscillating normal velocity bleed boundary condition to be specified.

    region   Bleed region number from .cgd file
amp Amplitude of the normal velocity oscillation (ft/sec)
freq Frequency of the oscillation (Hz)
phase Phase offset of the oscillation (deg)

BLEED FORCING was designed to be used on its own, independently of the other bleed modes. However, when BLEED FORCING is used in the same bleed region as another BLEED keyword, the specified oscillatory bleed velocity will be added to the bleed velocity computed for the other bleed mode.


    region   Bleed region number from .cgd file
temp   Wall temperature (°R)

This keyword may be used to explicitly turn bleed off in a specific bleed region, and to treat the boundary as a viscous solid wall.

BLEED AEDC region dstar por aspect

    region   Bleed region number from .cgd file
dstar Displacement thickness at start of bleed region (in)
por Porosity
aspect Bleed hole aspect ratio (i.e., ratio of bleed hole diameter to wall thickness)

This bleed mode is only available for structured grids.

When the AEDC keyword is specified, the bleed region uses the AEDC wind tunnel wall correction correlations. This model, based on the work of Martin, Sickles, and Stanley [Martin, F. W., Sickles, W. L., and Stanley, S. A., "Transonic Wind Tunnel Wall Interference Analysis for the Space Shuttle Launch Vehicle," AIAA Paper 93-0420], is hardwired for AEDC wind tunnels, and is not intended for general use. It assumes the following:


Last updated 1 Apr 2016