Water Injection Model Results
Last updated 2007-09-18 11:15 PDT

Water Injection Model Results

The current model is parameterized with ambient temperature, ambient pressure, relative humidity, injection fluid composition (water vs. methanol percentage) and fluid temperature. It assumes a fixed wet air mass (100 g), and computes the composition of that wet air using ambient temperature and relative humidity.

This model answers many questions, such as the following.

  1. What is the maximum amount of water that can be vaporized given a particular inlet air temperature?

  2. How much cooling effect will result from maximum vaporization?

  3. How much dilution of the intake charge results from the vaporized fluid? (In other words, how much oxygen is displaced by water vapor?)

  4. What is the net effect of cooling and dilution? Is there a charge density benefit from water injection?

Limitations

Before we try to answer these questions, we should make sure we know the major shortcomings and assumptions of the model. First, it assumes complete vaporization is possible when injecting the specified mass of liquid. In reality, less than the saturation amount will be vaporized. How much? If I knew, I'd put it in the model. (Maybe I'll parameterize that, too, so it can be an input). This effect is probably benign, in that it reduces all effects proportionately.

Second, it assumes that the energy for vaporizing the fluid all comes from the intake air. This is almost always incorrect, as some of the liquid will almost certainly wet a hot surface in the intake tract, say the manifold, and pick up energy there. This will cause an increase in charge volume without its beneficial cooling effect, so is a bad thing and the model is overly optmistic in this regard. How much error will be caused by this effect? This is completely installation dependent, so there is no theoretical way to estimate how large the error will be; it must be determined empirically for each case.

If you have good atomization, this will help with vaporization considerable and avoid these first two problems.

Third, it assumes that the vapor pressure for methanol is infinitely higher than that for water, and thus assumes complete vaporization of the injected liquid, even for huge quantities of methanol. This is a shortcoming in the model that may be addressed in the future, but for now you must avoid high proportions of methanol in the intake liquid mixture.

Analysis

What is the maximum amount of water that can be vaporized given a particular inlet air temperature? See the column labelled Mass H2O. This indicates in grams how much water can be vaporized into 100 grams of air at the given inlet temperature. Way over on the right is the air-liquid ratio column, indicating the relative mass ratios of the injected liquid and air. Notice that for cool air (Ti < 25°C), you are already near saturation in terms of ALR, even in dry air; but for hot non-intercooled air, you can squirt in quite a bit.

How much cooling effect will result from maximum vaporization? The dT (delta temperature) column indicates how much the temperature drops due to vaporization of the injected fluid. Look at the O2 Cool column. This is the fractional improvement in charge density due to this cooling effect. All other things held constant, this is the increase in HP you would feel.

How much dilution of the intake charge results from the vaporized fluid? (In other words, how much oxygen is displaced by water vapor?) Look at the O2 Dil column and you see the fractional decrease in charge density due to air being displaced by water vapor. Note that this is referenced to ambient air, not corrected back to standard conditions. Dry air provides the worst case (we are vaporizing the most water per volume of air), so look at the top table. We see that HP would be reduced to 86% for an inlet temperature of 300°C with 10:1 water injection.

What is the net effect of cooling and dilution? Take the previous two answers and multiply them out to get the answer, it's in the column labelled O2 Final. For hot intake charges, the effect is quite considerable, so you can readily see why water injection works so well on non-intercooled engines or those with marginal coolers.

As an example, using the 50% RH table, if you had a non-intercooled engine with post-turbo charge temperatures of about 200°C producing 200 WHP, you could inject a 16:1 air to water ratio mix and get 200*1.221 = 244 WHP.

Is there a charge density benefit from water injection? The answer is almost always yes. To answer this question definitively, you must examine the assumptions above and have reasonable input from them. For example, if your injector sprays the water stream directly on a hot part of the manifold, you'll see very little direct charge cooling effect, but you'll see a considerable increase in the H2O portion of charge volume. If this is bad enough, it can overwhelm the benefits, in very much the same way as running a turbocharger at a very high pressure ratio.

Results Tables

   T ambient  =  21.0°C
   P ambient  = 101.325 kPa
   Methanol   =   0.0% by mass
   Temp water =  21.0°C
   RH         =   0.0%
   Mass air   = 100.0 g (100.00g air, 0.00g H2O)

      Ti  Mass  Mass    Te    dT   Temp      O2     O2     O2    H2O      A:L
      °C   H2O  Meth    °C     °   Frac     Dil   Cool  Final     VP    Ratio
     --- ----- -----   ---   ---  -----   -----  -----  -----  -----  -------
       0  0.24  0.00    -6    -6  0.979   0.996  1.017  1.013   0.39  419.7:1
      25  0.68  0.00     9   -16  0.945   0.989  1.046  1.035   1.10  146.4:1
      50  1.31  0.00    18   -32  0.902   0.979  1.085  1.063   2.09   76.2:1
      75  2.05  0.00    25   -50  0.858   0.968  1.129  1.093   3.23   48.8:1
     100  2.85  0.00    31   -69  0.815   0.956  1.174  1.122   4.43   35.1:1
     125  3.68  0.00    35   -90  0.774   0.944  1.219  1.151   5.67   27.1:1
     150  4.55  0.00    39  -111  0.737   0.932  1.264  1.178   6.91   22.0:1
     175  5.43  0.00    42  -133  0.703   0.920  1.308  1.203   8.14   18.4:1
     200  6.33  0.00    45  -155  0.672   0.908  1.352  1.227   9.36   15.8:1
     225  7.24  0.00    47  -178  0.643   0.896  1.394  1.249  10.57   13.8:1
     250  8.16  0.00    49  -201  0.616   0.884  1.435  1.269  11.75   12.3:1
     275  9.09  0.00    51  -224  0.591   0.873  1.476  1.288  12.92   11.0:1
     300 10.02  0.00    53  -247  0.568   0.861  1.515  1.305  14.06   10.0:1

   Methanol   =   0.0% by mass
   RH         =  50.0%
   Mass air   = 100.0 g (99.24g air, 0.76g H2O)

      Ti  Mass  Mass    Te    dT   Temp      O2     O2     O2    H2O      A:L
      °C   H2O  Meth    °C     °   Frac     Dil   Cool  Final     VP    Ratio
     --- ----- -----   ---   ---  -----   -----  -----  -----  -----  -------
       0  0.00  0.00     0     0  1.000   1.000  1.000  1.000   0.59    0.0:1
      25  0.37  0.00    16    -9  0.971   0.994  1.024  1.018   1.82  273.3:1
      50  1.08  0.00    24   -26  0.920   0.983  1.069  1.051   2.96   92.5:1
      75  1.87  0.00    30   -45  0.870   0.971  1.115  1.083   4.19   53.5:1
     100  2.70  0.00    35   -65  0.824   0.958  1.162  1.114   5.45   37.0:1
     125  3.56  0.00    38   -87  0.782   0.946  1.209  1.143   6.72   28.1:1
     150  4.45  0.00    42  -108  0.744   0.933  1.255  1.171   7.99   22.5:1
     175  5.35  0.00    44  -131  0.708   0.921  1.300  1.197   9.25   18.7:1
     200  6.26  0.00    47  -153  0.676   0.909  1.344  1.221  10.49   16.0:1
     225  7.18  0.00    49  -176  0.647   0.897  1.386  1.243  11.71   13.9:1
     250  8.10  0.00    51  -199  0.619   0.885  1.428  1.264  12.91   12.3:1
     275  9.04  0.00    53  -222  0.594   0.873  1.469  1.283  14.08   11.1:1
     300  9.97  0.00    54  -246  0.571   0.862  1.508  1.300  15.23   10.0:1

   Methanol   =  50.0% by mass
   RH         =  50.0%
   Mass air   = 100.0 g (99.24g air, 0.76g H2O)

      Ti  Mass  Mass    Te    dT   Temp      O2     O2     O2    H2O      A:L
      °C   H2O  Meth    °C     °   Frac     Dil   Cool  Final     VP    Ratio
     --- ----- -----   ---   ---  -----   -----  -----  -----  -----  -------
       0  0.00  0.00     0     0  1.000   1.000  1.000  1.000   0.59    0.0:1
      25  0.28  0.28    15   -10  0.967   0.993  1.027  1.020   1.69  177.5:1
      50  0.81  0.81    21   -29  0.911   0.980  1.075  1.054   2.52   62.0:1
      75  1.37  1.37    26   -49  0.860   0.967  1.124  1.087   3.39   36.5:1
     100  1.95  1.95    30   -70  0.813   0.953  1.173  1.118   4.26   25.6:1
     125  2.55  2.55    33   -92  0.770   0.940  1.220  1.147   5.14   19.6:1
     150  3.17  3.17    36  -114  0.731   0.926  1.267  1.173   6.01   15.8:1
     175  3.79  3.79    39  -136  0.696   0.913  1.312  1.198   6.87   13.2:1
     200  4.42  4.42    41  -159  0.664   0.900  1.356  1.221   7.71   11.3:1
     225  5.05  5.05    43  -182  0.634   0.887  1.399  1.242   8.53    9.9:1
     250  5.68  5.68    45  -205  0.607   0.875  1.441  1.261   9.33    8.8:1
     275  6.32  6.32    46  -229  0.582   0.863  1.482  1.279  10.12    7.9:1
     300  6.97  6.97    48  -252  0.559   0.851  1.521  1.295  10.89    7.2:1

   Methanol   =   0.0% by mass
   RH         = 100.0%
   Mass air   = 100.0 g (98.47g air, 1.53g H2O)

      Ti  Mass  Mass    Te    dT   Temp      O2     O2     O2    H2O      A:L
      °C   H2O  Meth    °C     °   Frac     Dil   Cool  Final     VP    Ratio
     --- ----- -----   ---   ---  -----   -----  -----  -----  -----  -------
       0  0.00  0.00     0     0  1.000   1.000  1.000  1.000   0.59    0.0:1
      25  0.12  0.00    22    -3  0.991   0.998  1.008  1.006   2.65  854.1:1
      50  0.89  0.00    29   -21  0.934   0.986  1.056  1.041   3.89  112.2:1
      75  1.72  0.00    34   -41  0.881   0.973  1.104  1.075   5.19   58.2:1
     100  2.58  0.00    38   -62  0.833   0.960  1.153  1.107   6.49   38.8:1
     125  3.46  0.00    41   -84  0.789   0.947  1.200  1.137   7.80   28.9:1
     150  4.36  0.00    44  -106  0.750   0.935  1.247  1.165   9.10   22.9:1
     175  5.27  0.00    47  -128  0.713   0.922  1.292  1.191  10.38   19.0:1
     200  6.19  0.00    49  -151  0.681   0.909  1.336  1.215  11.63   16.2:1
     225  7.12  0.00    51  -174  0.650   0.897  1.380  1.238  12.87   14.1:1
     250  8.05  0.00    53  -197  0.623   0.885  1.422  1.259  14.07   12.4:1
     275  8.99  0.00    54  -221  0.597   0.874  1.462  1.278  15.25   11.1:1
     300  9.93  0.00    56  -244  0.574   0.862  1.502  1.295  16.41   10.1:1

      Ti        = Temperature of input air in °C.
      Mass H2O  = Optimized ideal mass of water which produces
                  partial pressure == vapor pressure @ Te.  This is
                  the maximum amount of water that can be vaporized;
                  any more will be liquid.
      Mass Meth = Mass of methanol injected in solution with water.
      Te        = Equilibrium temperature of evaporated mix in °C.
      dT        = Change in temperature in °.
      Temp Frac = Relative change in input air temperature.
      O2 Dil    = Concentration due to dilution with water vapor.

      The next two are relative to Ti, not an absolute temperature!

      O2 Cool   = Consequent concentration of O2 due to cooling.
      O2 Final  = Final concentration of O2 from both factors.
                  This is the important column, as it tells us
                  the relative intercooling effect of vaporizing
                  water injected into the intake tract.

      H2O VP    = Vapor pressure of H2O at Te.
      A:L Ratio = Mass ratio of air to liquid.
 
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