ng-model is not updated on keydown event as expected

I am trying to write unit test to test my directive. When I invoke keydown event ng-model is not updated. How can I make changes to ng-model from unit test?

My spec file is given below: describe('validNumber', function () {

var scope, elem, compiled, html, usageScenarioModel;

var triggerKeyDown = function (element, keyCode) {
    var e = angular.element.Event('keydown');
    e.which = keyCode;
    element.trigger(e);
};



beforeEach(function(){
    html = '<input type="number" valid-number ng-model="values[0].percentage"/>';

    inject(function($compile, $rootScope, _model_){
        model = _model_;
        scope = $rootScope.$new();
        elem = angular.element(html);
        scope.model = _model_;
        scope.model.values =  [{percentage:0}]};
        compiled = $compile(elem);
        compiled(scope);
        scope.$digest();
    })
});

it('should disable user to type non-numerical value into field', function(){
    triggerKeyDown(elem, 50);
    scope.$digest();
    expect(elem.val()).toBe(2);
});

});