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OpenStudio Model API doesn't provide methods to access this information directly but you can use the SqlFile class outside of Model to do what you need to do. In Ruby it would look something like this.
sql = OpenStudio::SqlFile.new 'path/to/energyplusrun/eplusout.sql'
sql.execAndReturnFirstDouble("select Value from TabularDataWithStrings WHERE ReportName='HVACSizingSummary' and ReportForString='Entire Facility' and TableName='Zone Cooling' and ColumnName='Calculated Design Air Flow' and RowName='STORY 1 CORE THERMAL ZONE';").get
This is assuming your tabular html data looks something like the screenshot. You may adjust the names to get other data in a similar way.